Some Properties Of Two Types Of Fractional Partial Differential Equations

Fractional calculus is recognized as one of the best tools to describe longmemory processes.Due to modeling feasibility,fractional differential equations have received considerable attention in the last decades.The mathematical theory of fractional partial differential equations is still not as complete as PDEs’ classical theory.Effective general methods are required to be specifically developed for fractional differential equations.In chapter 2,we concern initial/boundary value problem for the Rayleigh-Stokes equation.We first established the existence and regularity properties of the solution given by the eigenfunction expansions.Second,we provide a stability estimate for inverse problem of determining a time-dependence source term by single point observation.In chapter 3,we consider maximum principle for -Hilfer fractional diffusion equations.The maximum principles for fractional differential operator are established by an inequality for -Hilfer fractional derivative of function 1)at its maximum point.As applications,we obtain uniqueness and a priori estimate of solution to the objective equations.